FROM HERE TO THERE. They are all two-player games.

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1 FROM HERE TO THERE These games are rather quick ones that provide practice in counting by various units. There are some strategies involved that become rather sophisticated but knowing the strategies is not required to play the games. Strategy just enhances the chance of a win. They are all two-player games. Game One: Getting to 100. Each player starts with ten dimes and ten pennies. Players take turns contributing one, two or three coins to the pot. On placing the coins in the pot, the player calls out the cumulative total after each coin s/he places. The person who puts in the coin to make the total value of the pot exactly one dollar is the winner. (Each player must place at least one penny in the pot during the course of the game which keeps it from being just a game of dimes and counting by tens.) Variations on this game: Play on a one-hundred chart that is big enough to place the coins right on the chart. Both players are placing their coins on the same chart. Play on a one-hundred chart by crossing out the numbers that are called. Each player uses a different color crayon and are crossing out the numbers are the same chart. With only plain or lined paper, write the numbers underneath each other in a list, each player using a different color, playing on the same list--again writing one, two or three numbers. Each of the games above practices counting by tens and ones, which is a valuable skill for all elementary students. The younger ones need to have reinforced the idea that when adding tens, the number in the ones place does not change. Although we may think this is obvious, to many of our students it is not and is worth discussion. Game Two: Getting to 1,000. This game is played without coins. Students play as in the third variation of game one, placing numbers on a list in two different colors. Players may choose to add one, two or three numbers, using ones, tens and hundreds. The player who is able to place exactly 1,000 on the list is the winner. Variations on this game: Start at a number greater than one and have the target number be greater than 1,000. Make the counting units 25, 50 and 100. Play with decimals rather than whole numbers (tenths, hundredths). Play with fractions (quarters and halves). All of these games are variations on a game where the units are all the same. The first one I saw was played with twelve toothpicks. Players on alternate turns were able to pick up one or two toothpicks on a turn. The person to pick up the last toothpick was the winner (or the loser). Playing this simpler game can help us develop generalized winning strategies for all such games.

3 The Solution Game Purpose: Mental math practice, use of properties of operations to solve problems. Materials: One deck of regular playing cards with picture cards removed. Set-up: The cards are placed in a stack at the center of the table (face-down). Five cards are removed from the stack, one at a time, and placed in a row face- up. A sixth card is removed from the stack and placed face up below the row of five. This card is called the solution card. Object of the Game: Find a path to the solution card using as many cards in the row as possible with any arithmetic operations. (Each card may be used only once.) Play: The first person to see a possible path to solution says, SOLUTION and tells the rest of the group what his/her path is. If he or she is correct, he/she wins the cards used for the path to solution AND the solution card itself. Replace all cards that have been taken (won) by new cards from the center stack. Play continues in this fashion until no cards are left. The player with the most cards at then end of the game is the winner. Variations: Use all the cards from ace through 6 and only half the cards from This makes the game a little easier. Require a minimum number of cards used for solution. Only solutions using at least three (or four, or five) cards is accepted. Create a deck of cards as follows. Make 3 cards for each of the numbers from 1 through 8; 2 cards for each of the numbers from 9 through17; and one card for each of the numbers from 18 through 25. (This last variation is based on a card game called KRYPTO. For decks already printed like this, buy the KRYPTO deck from a company called, Making People Happy at makingpeoplehappy.com. There is also a fraction supplement to the regular deck. ) The variations allow for differentiation. Small groups can be playing different versions at the same time.

4 Cooperation Materials: Index cards for each student. Each index card shows a number from 1 to 9. The cards are then punched and strung so students can hang them around their necks. Object: The object of the game is to have students join with other students to form expressions equal to a given target number within a given time. Scoring: At the end of each round, each student in a given expression scores the number of points equal to the number of people in the expression. Sample Game: Leader passes out a number card to each student. The number card is hung around the neck so that each student can see each other student s number. Round One: The leader announces a time limit; for example, two minutes, and a target number; for example, 12. Students then move around looking for other students with whom they can join to complete an expression (using addition, subtraction, multiplication, and/or division) whose value is 12. Below are examples of the numbers in an expression and how each team created the expression because 2 X = because (9/3) X 1 X 1 X 4 = because (6 X 5) divided by 3-9 X 2 X 6 = 12 The number of points for each student in the first expression is 4 because there are four students representing the expression. Therefore, the number of points for each student in the second expression is 5, and the score in the third expression is 6. Each student keeps track of his/her own points. The leader begins round two. Game continues for the time allotted. Students with the most points are the winners. There are usually lots of winners Suggestions: When played early in the year, it becomes clear who the leaders are. It is probably a good idea to give the most valuable number (1) to the least popular child. Then all of the expressions will want him/her The game changes as the students progress in their understanding of the properties of numbers, so it is best played at several different times during the year. If students are getting too hung up on addition and subtraction only, try offering bonus points for each multiplication and/or division in an expression. It is important to have each student participate in the saying of how his/her number belongs in the expression, rather than have one student do it all. Some students use their arms to create parenthesis around certain sections of the expressions. Other students stand on tables (use your judgment) with other students under the tables to express division It might be interesting to make one or two of the index cards wild cards. This game was first taught to me by my dear friend, the late Ginger Silverman. I do not know its origin. Mary Behr Altieri

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6 A Fraction/Decimal Variation of the Roll a Problem Game This game is played on a hand made grid indicating the addition of two fractions, as shown below. It is played with two number cubes. One of the cubes (know as the low cube) is numbered from 0 to 5. The other (the high cube) is numbered from 5 to 10. In this game if a 10 is rolled, it is wild and each player may use it as any digit from 0 through 9. + Each player has his or her own grid. A number cube is rolled. The sequence of rolls for this game is High, Low, High, Low. All players use the number that is rolled to fill in a space on the grid indicating a numerator or a denominator for either fraction. Once a number is placed it cannot be moved. All players must place the number after each roll before the next number is rolled. When four numbers have been rolled, the grid will be complete and each player evaluates the resulting sum of the two fractions. The player with the sum closest to one is the winner. NB: Any player who places a zero in the denominator will automatically lose. Another variation would be to add a fraction and a decimal.. + Variations: The person with the greatest, least or closest to some chosen sum is the winner. Change the operation to subtraction or multiplication. Change the sequence of the cubes rolled.

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10 Addenda&and&Citations& ThehundredchartstickersareavailablefromGraphpatch.com. Ifyougotothewebsite,youcandownloadanorderform theydonottakeorders directlyfromtheinternet. Althoughtheyshowonlyvariousoptionsofgraphgrids(whichmayalsointerest you),theydo&not&show hundredchart. Justwrite hundredchart ontheorder formwhereitaskswhatstyleyouwant.youcanordertheminpackagesof30oron arollof500.oryoucanmixandmatchpackagesofgraphgridsandhundreds charts.theminimumorderis$25,whichisthecostofonerollof500. Numbercubeswith0M5and5M10areveryexpensive.Itismuchlessexpensiveto buyblankwoodencubesandlabelthemyourself.oryoucandivideadeckofcards intotwopiles highandlow.ifyouwantazero,useapicturecard.putting5sin bothpilesmakesitalittlemoreinteresting. Thesmallblankflashcardsarefrom Pacon. IfyouGooglethatnameyouwillfind severalsourcesatvariousprices. Theinformationforthepremadedeckofcardsforthehighestdifficultylevelofthe SolutionGame(whichis Krypto )isonthesheetthathastheinstructionsforall levelsofthesolutiongame.onthewebsiteforkryptoyoucanalsofindoutifthe setof5numberscanbemanipulatedtoresultinthesolutionnumber.youcanalso choosewhetherornotyouwanttoknowwhatthesolutionis,orjustifitispossible. MakingPeopleHappyisreallythenameofthecompanyhttp://mphgames.com/ SourcesforCountingGamesUsed: BalloonRide, FamilyMath,JeanStenmark,VirginiaThompsonandRuthCossey, LawrenceHallofScience(EQUALSSERIES) Gettoadollarwithdimesandpennies,RealMath,(OpenCourt)SRAWright Group. Raceto100,TriMathlon,J.SallyandP.Sally,CRCPress,2003.

Mary Behr Altieri P/NW BOCES SW BOCES

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